Topology is the study of whether objects can be smoothly transformed into each other. Sometimes these `objects' are extremely abstract mathematical ideas, sometimes they're not: Can I uncoil this garden hose without removing the end from the bucket? Can I untangle these necklaces without undoing the clasps? Can I wrap this map of the world onto a globe? These are all problems of topology. Related topological questions appear across physics, where wave dispersion surfaces [1]}, knotted fluid flow lines [2]}, and electromagnetic fields [3]} can all be grouped according to whether, or not they can be smoothly transformed into one another.
